1. Field of the Invention
This invention is related to the field of electronic control systems. More particularly, this invention is related to a control system of the type based on microprocessors, for controlling electromechanical devices. It is particularly useful as a magnetic bearing control system for a magnetic bearing arrangement, such as the type used to levitate a rotating shaft.
2. Description of the Problem
The problem of lubrication and wear in moving mechanical parts is as old as the utilization of mechanical devices. Various schemes have been devised to eliminate or reduce either or both of these problems with varying degrees of success. One way of alleviating these problems in rotating machines is to use magnetic bearings. Magnetic bearings are well known. A magnetic bearing allows a movable member (a rotor) of a machine to rotate freely with very little friction. This lack of friction is achieved by suspending the movable member, usually a shaft, within a housing lined with magnetic devices, so that the shaft can rotate without touching any solid surfaces. The shaft is suspended or levitated by magnetic fields.
FIG. 1 illustrates a cross-section of an example magnetic bearing. In this case the movable member consists primarily of a shaft, 110, which runs perpendicular to the paper. A disk, 109, made of laminated magnetic material is fixed to shaft 110. Four magnets, 101, 102, 103, and 104, are attached to a housing and distributed around the disk, 109. Electrical coils 105, 106, 107, and 108, are wound around the magnets and control the magnetic fields. In most cases, the magnet/coil combinations work in pairs. For example, magnets 101 and 103 work as a pair to control levitation of the shaft in the up/down direction in the drawing, and magnets 102 and 104 likewise work as a pair to control movement in the left/right direction. The housing for this bearing is not shown so that the details of the bearing itself can be shown more clearly.
FIG. 2 is a longitudinal section of a rotor being suspended by three magnetic bearings. Normally, the entire assembly is contained in a housing, which is not shown for clarity. Item 201 is a shaft, which is situated along axis 202. Laminated disk 205 is acted upon by bearing 204, which is shown in simplified form for clarity, but in reality includes an arrangement of magnets like that shown in FIG. 1, and sensors which detect the displacement of the shaft along the two control axes. Assuming a driving motor is positioned to the right in this illustration, bearing 204 is called an “inboard” radial bearing. Likewise, bearing 203 acts on disk 206. Again, assuming a driving motor located down axis 202 to the right, magnetic bearing 203 is called an “outboard” radial bearing. Housing 207 contains what is commonly known as a “thrust” bearing, and contains two electrically controlled magnets, 209 and 210, as well as an appropriate position sensor. These magnets act on disk 208 to control movement and position of the shaft along the axis 202 from left to right. The magnetic bearing system shown in FIG. 2 is an example only. It is possible to devise bearing systems of other shapes, which may have more or fewer bearings and more or fewer magnets in a given bearing. Other types of magnets may be used. In some machines, a thrust bearing may not be needed, for example, when a motor coupling provides axial support. In some applications, only a magnetic bearing on one end of a shaft is used, for example, if the other end is supported by other means. U.S. Pat. Nos. 5,216,308; 5,347,190; 5,543,673; and 5,986,373 provide background and additional information on this and other example magnetic bearing systems, and are incorporated herein by reference.
Generally, sophisticated electronics are required to vary the amount of field produced by the magnets in an electromechanical device such as a magnetic bearing. Control signals are produced for the magnets in response to position signals in order to maintain the rotor in levitation regardless of changing loads and/or mechanical conditions. The present commercial practice for active magnetic bearing control systems is a design in which each axis to be controlled, typically two orthogonal radial directions and one axial (thrust) direction, possesses an independent proportional-integral (PI), proportional-derivative (PD) or proportional-integral-derivative (PID) controller. However, electromechanical devices like magnetic bearings are difficult to control because they are inherently unstable, and so they have found only limited use in industry.
A well-known technique for controlling stable electromechanical systems is to employ the concept of a “unified plant.” As an example, consider the control system of FIG. 3. The control system, 302, consists of PID controllers, 303, and a compensator, 304. In this approach, a signal from the plant, P, 301, is passed through a matrix of digital filters in the compensator. The multidimensional filter undoes to some extent the transmission characteristics of the multi-dimensional plant. The filter operates on a vector of error signals measured at point 305. The filtering allows the controller gains to be increased theoretically without limit for an ideal stable plant with no time delay or other nonlinearity. The extent to which these gains can actually be increased is limited by how well the filter approximates the plant inverse and by any constraints on the power output.
The system above works well with stable plants. However, many practical electromechanical systems exhibit open-loop instability. Magnetic bearings, for example, exhibit a type of open-loop instability called “negative stiffness.” Applying the unified plant approach to such a system is complicated due to the presence of this negative stiffness. To understand what is meant by negative stiffness, assume for the time being the absence of gravity. Allow a shaft to be balanced at its equilibrium position, as shown in FIG. 4. FIG. 4 shows a shaft, 401, and a magnetic bearing made up of four magnets, a left top (LT) magnet, 402, a right top (RT) magnet, 403, a left bottom (LB) magnet, 404, and a right bottom (RB) magnet, 405. If the bearing had positive stiffness, perturbations from equilibrium result in a restoring force that pulls the shaft back to equilibrium. The larger the perturbation, the stronger the restoring force. However, negative stiffness implies an unstable equilibrium. If the forces on the magnets are exactly balanced as shown in FIG. 4, any minute perturbation x causes a force F that grows with increasing distance from the equilibrium position until the shaft hits the stator (the stationary part of the magnetic bearing assembly). Magnetic bearings require a control force to overcome the effect of negative stiffness.
Some form of PI, PD or PID control is generally sufficient to overcome negative stiffness so that the shaft can be levitated. However, in order for the shaft to remain suspended under changing loads, the closed loop positive stiffness, and hence the feedback gains must be large. The resistance of the bearing to motion caused by changing loads is referred to as its “dynamics stiffness”. In uncompensated systems, the large feedback gains required for dynamic stiffness cause stability problems related to plant dynamics other than negative stiffness. This will be the case when non-linear dynamic characteristics (e.g., time-delay) and when cross-response structural resonances are present in the sensor bandwidth. Due to the above-described instability problems, current magnetic bearing control systems have major drawbacks. Such systems exhibit stability sensitivity and relatively narrow controller bandwidth in each direction. There are alternative approaches for improving dynamic stiffness that involve deriving an adequate, low-order model from measurements or simulation data. These are referred to as state-space models. This derivation is not straight-forward, and can require significant off-line time by a very skilled practitioner in the control theory and system identification fields. Automated design algorithms are often intractable for complex, highly dynamic, electromechanical systems. Therefore, control systems based on state-space models are difficult to design and expensive to use in commercial applications. What is needed is a new type of control system that can handle open-loop instability such as negative stiffness, but that can also be based on a unified plant so that the control system is more straightforward to adapt to various electromechanical arrangements.